1998/10/27 by Ross Geoghegan, Geoghegan, Ross, Andrew Nicas +1
Mathematics · #19B99 #57R20 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.GT #math.KT #msc:19B99 #msc:57R20
paper · pdf · doi:10.48550/arxiv.math/9810151
50 pages, To appear in "K-Theory"
arxiv created 1998/10/27 · openalex publication_date 1998/10/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define a "circle Euler characteristic" of a circle action on a compact manifold or finite complex X. It lies in the first Hochschild homology group of ZG where G is the fundamental group of X. It is analogous in many ways to the ordinary Euler characteristic. One application is an intuitively satisfying formula for the Euler class (integer coefficients) of the normal bundle to a smooth circle action without fixed points on a manifold. In the special case of a 3-dimensional Seifert fibered space, this formula is particularly effective. \~